Abstract

Mode-division multiplexing is a promising and cost-effective way to increase the communication capability of integrated photonic circuits, for both classical and quantum information processing. To construct large-scale on-chip multimode routing systems, the multimode waveguide crossing is one of the key components. However, there have been only a few dual-mode waveguide crossings reported, which can support merely two waveguide modes or two crossing channels. This severely limits the density and capacity of multimode routing systems. Here we demonstrate for the first time, to the best of our knowledge, a universal multimode waveguide star crossing based on transformation optics, which can handle, in principle, any number of waveguide modes and any number of crossing channels as well. The structure is transformed from a Maxwell fisheye and can realize aberration-free imaging for each waveguide mode. A gray-scale electron-beam lithography is adopted to fabricate it on a commercial silicon-on-insulator wafer. The proposed multimode waveguide star crossing has little loss and low crosstalk throughout an ultra-broad wavelength range of 400  nm. Our study paves the way for realizing highly integrated and large capacity on-chip multimode routing and communication systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article

Corrections

5 December 2018: A typographical correction was made to the author listing.


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2018 (4)

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photon. Res. 6, 660–665 (2018).
[Crossref]

H. Xu and Y. Shi, “Metamaterial-based Maxwell’s fisheye lens for multimode waveguide crossing,” Laser Photon. Rev. 12, 1800094 (2018).
[Crossref]

O. Bitton, R. Bruch, and U. Leonhardt, “Two-dimensional Maxwell fisheye for integrated optics,” Phys. Rev. Appl. 10, 044059 (2018).
[Crossref]

2017 (1)

2016 (4)

G. Chen, Y. Yu, and X. Zhang, “Monolithically mode division multiplexing photonic integrated circuit for large-capacity optical interconnection,” Opt. Lett. 41, 3543–3546 (2016).
[Crossref]

H. Xu and Y. Shi, “Dual-mode waveguide crossing utilizing taper-assisted multimode-interference couplers,” Opt. Lett. 41, 5381–5384 (2016).
[Crossref]

L. T. Feng, M. Zhang, Z. Y. Zhou, M. Li, X. Xiong, L. Yu, B. S. Shi, G. P. Guo, D. X. Dai, X. F. Ren, and G. C. Guo, “On-chip coherent conversion of photonic quantum entanglement between different degrees of freedom,” Nat. Commun. 7, 11985 (2016).
[Crossref]

Y. Kim, S.-Y. Lee, J.-W. Ryu, I. Kim, J.-H. Han, H.-S. Tae, M. Choi, and B. Min, “Designing whispering gallery modes via transformation optics,” Nat. Photonics 10, 647–652 (2016).
[Crossref]

2015 (1)

L. Xu and H. Chen, “Conformal transformation optics,” Nat. Photonics 9, 15–23 (2015).
[Crossref]

2014 (2)

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

X. Li, H. Xu, X. Xiao, Z. Li, J. Yu, and Y. Yu, “Demonstration of a highly efficient multimode interference based silicon waveguide crossing,” Opt. Commun. 312, 148–152 (2014).
[Crossref]

2013 (3)

2012 (3)

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref]

Q. Wu, J. P. Turpin, and D. H. Werner, “Integrated photonic systems based on transformation optics enabled gradient index devices,” Light Sci. Appl. 1, e38 (2012).
[Crossref]

P. Markov, J. G. Valentine, and S. M. Weiss, “Fiber-to-chip coupler designed using an optical transformation,” Opt. Express 20, 14705–14713 (2012).
[Crossref]

2011 (1)

T. Zentgraf, Y. Liu, M. H. Mikkelsen, J. Valentine, and X. Zhang, “Plasmonic Luneburg and Eaton lenses,” Nat. Nanotechnol. 6, 151–155 (2011).
[Crossref]

2010 (13)

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

M. Schmiele, V. S. Varma, C. Rockstuhl, and F. Lederer, “Designing optical elements from isotropic materials by using transformation optics,” Phys. Rev. A 81, 033837 (2010).
[Crossref]

T. Zentgraf, J. Valentine, N. Tapia, J. Li, and X. Zhang, “An optical ‘Janus’ device for integrated photonics,” Adv. Mater. 22, 2561–2564 (2010).
[Crossref]

N. Kundtz and D. R. Smith, “Extreme-angle broadband metamaterial lens,” Nat. Mater. 9, 129–132 (2010).
[Crossref]

H. F. Ma and T. J. Cui, “Three-dimensional broadband and broad-angle transformation-optics lens,” Nat. Commun. 1, 124 (2010).
[Crossref]

D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18, 21238–21251 (2010).
[Crossref]

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delage, D. X. Xu, S. Janz, A. Densmore, and T. J. Hall, “Subwavelength grating crossings for silicon wire waveguides,” Opt. Express 18, 16146–16155 (2010).
[Crossref]

J. B. Feng, Q. Q. Li, and S. S. Fan, “Compact and low cross-talk silicon-on-insulator crossing using a periodic dielectric waveguide,” Opt. Lett. 35, 3904–3906 (2010).
[Crossref]

X. Chen, C. Li, C. K. Y. Fung, S. M. G. Lo, and H. K. Tsang, “Apodized waveguide grating couplers for efficient coupling to optical fibers,” IEEE Photon. Technol. Lett. 22, 1156–1158 (2010).
[Crossref]

Z. Chang, X. M. Zhou, J. Hu, and G. K. Hu, “Design method for quasi-isotropic transformation materials based on inverse Laplace’s equation with sliding boundaries,” Opt. Express 18, 6089–6096 (2010).
[Crossref]

Y. G. Ma, N. Wang, and C. K. Ong, “Application of inverse, strict conformal transformation to design waveguide devices,” J. Opt. Soc. Am. A 27, 968–972 (2010).
[Crossref]

A. Schleunitz and H. Schift, “Fabrication of 3D nanoimprint stamps with continuous reliefs using dose-modulated electron beam lithography and thermal reflow,” J. Micromech. Microeng. 20, 095002 (2010).
[Crossref]

U. Levy, B. Desiatov, I. Goykhman, T. Nachmias, A. Ohayon, and S. E. Meltzer, “Design, fabrication, and characterization of circular Dammann gratings based on grayscale lithography,” Opt. Lett. 35, 880–882 (2010).
[Crossref]

2009 (4)

P. Sanchis, P. Villalba, F. Cuesta, A. Hakansson, A. Griol, J. V. Galan, A. Brimont, and J. Marti, “Highly efficient crossing structure for silicon-on-insulator waveguides,” Opt. Lett. 34, 2760–2762 (2009).
[Crossref]

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[Crossref]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[Crossref]

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref]

2007 (3)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224–227 (2007).
[Crossref]

J. Kim, D. C. Joy, and S. Y. Lee, “Controlling resist thickness and etch depth for fabrication of 3D structures in electron-beam grayscale lithography,” Microelectron. Eng. 84, 2859–2864 (2007).
[Crossref]

J.-J. Yang, Y.-S. Liao, and C.-F. Chen, “Fabrication of long hexagonal micro-lens array by applying gray-scale lithography in micro-replication process,” Opt. Commun. 270, 433–440 (2007).
[Crossref]

2006 (4)

R. Murali, D. K. Brown, K. P. Martin, and J. D. Meindl, “Process optimization and proximity effect correction for gray scale e-beam lithography,” J. Vac. Sci. Technol. B 24, 2936 (2006).
[Crossref]

J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science 312, 1780–1782 (2006).
[Crossref]

U. Leonhardt, “Optical conformal mapping,” Science 312, 1777–1780 (2006).
[Crossref]

B. Fuchs, O. Lafond, S. Rondineau, and M. Himdi, “Design and characterization of half Maxwell fish-eye lens antennas in millimeter-waves,” IEEE Trans. Microw. Theory Tech. 54, 2292–2300 (2006).
[Crossref]

2005 (1)

C. M. Waits, B. Morgan, M. Kastantin, and R. Ghodssi, “Microfabrication of 3D silicon MEMS structures using gray-scale lithography and deep reactive ion etching,” Sens. Actuators A 119, 245–253 (2005).
[Crossref]

2004 (1)

B. Morgan, C. M. Waits, J. Krizmanic, and R. Ghodssi, “Development of a deep silicon phase Fresnel lens using gray-scale lithography and deep reactive ion etching,” J. Microelectromech. Syst. 13, 113–120 (2004).
[Crossref]

2003 (1)

C. M. Waits, A. Modafe, and R. Ghodssi, “Investigation of gray-scale technology for large area 3D silicon MEMS structures,” J. Micromech. Microeng. 13, 170–177 (2003).
[Crossref]

1994 (1)

H. Rosu and M. Reyes, “Electromagnetic modes of Maxwell fisheye lens,” Il Nuovo Cimento D 16, 517–522 (1994).
[Crossref]

Acin, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref]

Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref]

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref]

Bartal, G.

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
[Crossref]

Bergmen, K.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
[Crossref]

Bitton, O.

O. Bitton, R. Bruch, and U. Leonhardt, “Two-dimensional Maxwell fisheye for integrated optics,” Phys. Rev. Appl. 10, 044059 (2018).
[Crossref]

Bock, P. J.

Bonneau, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref]

Brimont, A.

Brown, D. K.

R. Murali, D. K. Brown, K. P. Martin, and J. D. Meindl, “Process optimization and proximity effect correction for gray scale e-beam lithography,” J. Vac. Sci. Technol. B 24, 2936 (2006).
[Crossref]

Bruch, R.

O. Bitton, R. Bruch, and U. Leonhardt, “Two-dimensional Maxwell fisheye for integrated optics,” Phys. Rev. Appl. 10, 044059 (2018).
[Crossref]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat. Photonics 1, 224–227 (2007).
[Crossref]

Cardenas, J.

L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics 3, 461–463 (2009).
[Crossref]

Chan, C. T.

H. Chen, C. T. Chan, and P. Sheng, “Transformation optics and metamaterials,” Nat. Mater. 9, 387–396 (2010).
[Crossref]

Y. Lai, J. Ng, H. Chen, D. Han, J. Xiao, Z. Q. Zhang, and C. T. Chan, “Illusion optics: the optical transformation of an object into another object,” Phys. Rev. Lett. 102, 253902 (2009).
[Crossref]

Chang, W.

Chang, Z.

Cheben, P.

Chen, C. P.

L. W. Luo, N. Ophir, C. P. Chen, L. H. Gabrielli, C. B. Poitras, K. Bergmen, and M. Lipson, “WDM-compatible mode-division multiplexing on a silicon chip,” Nat. Commun. 5, 3069 (2014).
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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. Design of a TF-MWC by the ABCM method. (a) Polar coordinates of a MF with a radius R . For an N -channel multimode star crossing, we set R = 25    μm ( N = 4 , M = 3 ) and R = 34    μm ( N = 5 , M = 4 ). One sector ring in the coordinates, shown by the red ( N = 4 , M = 3 ) or orange ( N = 5 , M = 4 ) line, is set as the original object, with 3    μm r R and π / 8 φ π / 8 or π / 10 φ π / 10 . Its boundary grid line at φ = ± π / 8 or φ = ± π / 10 is partially cut open from r = R to r = 16.9    μm ( N = 4 M = 3 ) or r = 22    μm ( N = 5 M = 4 ), specified by the red or orange dashed line, respectively. (b), (c) Coordinates transformed by the ABCM method for the N = 4 , M = 3 and N = 5 , M = 4 cases, respectively. They are obtained by repeating the conformal mapping of the sector ring shown by the red ( N = 4 , M = 3 ) or orange ( N = 5 , M = 4 ) line in panel (a). The index ratio between the center and edge of a MF decreases from 2 1 to 1 1 accurately by optimizing the shape. (d) Index distribution of a MF. The maximum index is set to be 2.83, which is the effective index of a 220 nm thick silicon slab waveguide on a SOI wafer. (e), (f) Index distributions of the transformed MFs for N = 4 , M = 3 and N = 5 , M = 4 , respectively.
Fig. 2.
Fig. 2. Propagation of the lowest three order TE modes in the four-channel D-MWC, simulated by 3D FDTD. Efficiency histograms of the (a)  TE 0 , (b)  TE 1 , and (c)  TE 2 mode propagation for 1550 nm wavelength are shown. The width of every multimode waveguide is 2 μm. The profiles of the H z field component for (d)  TE 0 , (e)  TE 1 , and (f)  TE 2 mode propagation. The labels T, C, V, and AC represent the throughout port, oblique crossing port, vertical crossing port, and anti-oblique crossing port, respectively.
Fig. 3.
Fig. 3. Propagation of the lowest three order TE modes in the four-channel TF-MWC, simulated by 3D FDTD. Efficiency histograms of (a)  TE 0 , (b)  TE 1 , and (c)  TE 2 mode propagation for 1550 nm wavelength. The input/output waveguide width is 2 μm. The profiles of the H z field component for (d)  TE 0 , (e)  TE 1 , and (f)  TE 2 mode propagation. The port labels are the same as those in Fig. 2. Simulation results show that the transmission efficiencies of all three modes are above 95.3% (0.21 dB) and crosstalk values to other modes or other ports are all below 37    dB .
Fig. 4.
Fig. 4. Calculated spectra of the four-channel three-mode TF-MWC and corresponding D-MWC by 3D FDTD simulations. The theoretical spectra of the TF-MWC for the (a)  TE 0 , (b)  TE 1 , and (c)  TE 2 modes. The theoretical spectra of the D-MWC for the (d)  TE 0 , (e)  TE 1 , and (f)  TE 2 modes.
Fig. 5.
Fig. 5. Characterization of the fabricated device. (a) The microscopic view of the fabricated device, including the TF-MWC, grating couplers, and mode multiplexer/demultiplexer. (b) Magnified microscopic view of the TF-MWC fabricated by gray-scale E-beam lithography. (c), (d) SEM photos of the grating coupler and asymmetric directional coupler structure of the mode multiplexer/demultiplexer. (e) 3D profile of the TF-MWC, measured by AFM.
Fig. 6.
Fig. 6. Experimental results of the four-channel three-mode D-MWC and four-channel three-mode TF-MWC at 1550 nm wavelength. (a)–(c) Measured efficiency histograms of the D-MWC. The transmission efficiencies for the TE 0 , TE 1 , and TE 2 modes are 71.7% ( 1.44    dB ), 21.4% ( 6.69    dB ), and 1.5% ( 18.21    dB ), respectively. (d)–(f) Measured efficiency histograms of the TF-MWC. The transmission efficiencies for the TE 0 , TE 1 , and TE 2 modes are 87.3% ( 0.59    dB ), 61.4% ( 2.12    dB ), and 53.9% ( 2.68    dB ), respectively. The crosstalk values to other modes or other ports are all below 19.5    dB .
Fig. 7.
Fig. 7. Measured spectra of the four-channel three-mode TF-MWC and the corresponding D-MWC. The measured spectra of the TF-MWC for the (a)  TE 0 , (b)  TE 1 , and (c)  TE 2 modes. The measured spectra of the D-MWC for the (d)  TE 0 , (e)  TE 1 , and (f)  TE 2 modes.